n-COLOR OVERPARTITIONS, TWISTED DIVISOR FUNCTIONS, AND ROGERS-RAMANUJAN IDENTITIES

Print ISSN: 0972-7752 | Online ISSN: | Total Downloads : 421

Volume : 6 , Issue : 2
DOI:
Author :
Jeremy Lovejoy (CNRS, LIAFA, Universit´e Denis Diderot, 2, Place Jussieu Case 7014, F-75251 Paris Cedex 05, France)
Olivier Mallet (CNRS, LIAFA, Universit´e Denis Diderot, 2, Place Jussieu Case 7014, F-75251 Paris Cedex 05, France)

Abstract

In the early 90’s Andrews discussed a certain q-series whose coefficients are determined by a twisted divisor function. We provide several other examples of this nature. All of these q-series can be interpreted combinatorially in terms of n-color overpartitions, as can some closely related series occurring in identities of the Rogers-Ramanujan type.

Keywords and Phrases

Partitions, overpartitions, n-color overpartitions, real quadratic fields, Bailey pairs, Rogers-Ramanujan identities.

A.M.S. subject classification

11P81, 05A17, 33D15.

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